{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:EOKH2NF4WW4UHVZRHPGKGH6EYZ","short_pith_number":"pith:EOKH2NF4","schema_version":"1.0","canonical_sha256":"23947d34bcb5b943d7313bcca31fc4c64a6400d385a3fb4800b0c344ec62aae8","source":{"kind":"arxiv","id":"2403.09876","version":1},"attestation_state":"computed","paper":{"title":"Which shapes can appear in a Curve Shortening Flow Singularity?","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Alex Moon, Aris Lemmenes, Edgar Gevorgyan, Ellie DeCleene, Evan Patrick Davis, Paige Ellingson, Sigurd Angenent, Tyler Joseph Tommasi, Yamin Zhou, Ziheng Feng","submitted_at":"2024-03-14T21:13:38Z","abstract_excerpt":"We study possible tangles that can occur in singularities of solutions to plane Curve Shortening Flow. We exhibit solutions in which more complicated tangles with more than one self-intersection disappear into a singular point. It seems that there are many examples of this kind and that a complete classification presents a problem similar to the problem of classifying all knots in $\\mathbb R^3$. As a particular example, we introduce the so-called $n$-loop curves, which generalize Matt Grayson's Figure-Eight curve, and we conjecture a generalization of the Coiculescu-Schwarz asymptotic bow-tie "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2403.09876","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2024-03-14T21:13:38Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"e849932ff435f88200636d3d9af7d2d8d0884214c669ef96feaebce4d4fa01b4","abstract_canon_sha256":"2df61f3b66f957a69d11d87c42e107d73dc41a214b619b0a11c024b382d0eb22"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:56:26.773438Z","signature_b64":"TV4qa2vro6oJ42pCm9SxTMXkOkDPKXJx06rwOFrYLfR8VkuIWreuAZqZ5P5ufRkOyQ0jNnYGqZPDY8FPTXKKDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23947d34bcb5b943d7313bcca31fc4c64a6400d385a3fb4800b0c344ec62aae8","last_reissued_at":"2026-07-05T07:56:26.773054Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:56:26.773054Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Which shapes can appear in a Curve Shortening Flow Singularity?","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Alex Moon, Aris Lemmenes, Edgar Gevorgyan, Ellie DeCleene, Evan Patrick Davis, Paige Ellingson, Sigurd Angenent, Tyler Joseph Tommasi, Yamin Zhou, Ziheng Feng","submitted_at":"2024-03-14T21:13:38Z","abstract_excerpt":"We study possible tangles that can occur in singularities of solutions to plane Curve Shortening Flow. We exhibit solutions in which more complicated tangles with more than one self-intersection disappear into a singular point. It seems that there are many examples of this kind and that a complete classification presents a problem similar to the problem of classifying all knots in $\\mathbb R^3$. As a particular example, we introduce the so-called $n$-loop curves, which generalize Matt Grayson's Figure-Eight curve, and we conjecture a generalization of the Coiculescu-Schwarz asymptotic bow-tie "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.09876","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2403.09876/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2403.09876","created_at":"2026-07-05T07:56:26.773108+00:00"},{"alias_kind":"arxiv_version","alias_value":"2403.09876v1","created_at":"2026-07-05T07:56:26.773108+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.09876","created_at":"2026-07-05T07:56:26.773108+00:00"},{"alias_kind":"pith_short_12","alias_value":"EOKH2NF4WW4U","created_at":"2026-07-05T07:56:26.773108+00:00"},{"alias_kind":"pith_short_16","alias_value":"EOKH2NF4WW4UHVZR","created_at":"2026-07-05T07:56:26.773108+00:00"},{"alias_kind":"pith_short_8","alias_value":"EOKH2NF4","created_at":"2026-07-05T07:56:26.773108+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2508.19667","citing_title":"Survey of Specialized Large Language Model","ref_index":49,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EOKH2NF4WW4UHVZRHPGKGH6EYZ","json":"https://pith.science/pith/EOKH2NF4WW4UHVZRHPGKGH6EYZ.json","graph_json":"https://pith.science/api/pith-number/EOKH2NF4WW4UHVZRHPGKGH6EYZ/graph.json","events_json":"https://pith.science/api/pith-number/EOKH2NF4WW4UHVZRHPGKGH6EYZ/events.json","paper":"https://pith.science/paper/EOKH2NF4"},"agent_actions":{"view_html":"https://pith.science/pith/EOKH2NF4WW4UHVZRHPGKGH6EYZ","download_json":"https://pith.science/pith/EOKH2NF4WW4UHVZRHPGKGH6EYZ.json","view_paper":"https://pith.science/paper/EOKH2NF4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2403.09876&json=true","fetch_graph":"https://pith.science/api/pith-number/EOKH2NF4WW4UHVZRHPGKGH6EYZ/graph.json","fetch_events":"https://pith.science/api/pith-number/EOKH2NF4WW4UHVZRHPGKGH6EYZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EOKH2NF4WW4UHVZRHPGKGH6EYZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EOKH2NF4WW4UHVZRHPGKGH6EYZ/action/storage_attestation","attest_author":"https://pith.science/pith/EOKH2NF4WW4UHVZRHPGKGH6EYZ/action/author_attestation","sign_citation":"https://pith.science/pith/EOKH2NF4WW4UHVZRHPGKGH6EYZ/action/citation_signature","submit_replication":"https://pith.science/pith/EOKH2NF4WW4UHVZRHPGKGH6EYZ/action/replication_record"}},"created_at":"2026-07-05T07:56:26.773108+00:00","updated_at":"2026-07-05T07:56:26.773108+00:00"}